[Colloquium] Theory Seminars at Computer Science

[Donna Brooms via Colloquium]

Combinatorics & Theoretical Seminar
 
Tuesday, April 18, 2017
Ryerson 251 @ 3pm

Andrej Bogdanov
Chinese University of Hong Kong
http://www.cs.washington.edu/homes/jrl/

Title: “Small bias requires large formulas”
A small-biased function is a randomized function whose distribution of truth-tables is small-biased. We show that known explicit lower bounds on the size of (1) general Boolean formulas, (2) Boolean formulas of fan-in two, (3) de Morgan formulas, as well as (4) correlation lower bounds against small de Morgan formulas apply to small-biased functions. As a consequence, any strongly explicit small-biased generator is subject to the best known explicit formula lower bounds in all these models.

On the other hand, we give a construction of a small-biased function that is tight with respect to lower bounds (1) and (2) for the relevant range of parameters. We interpret this construction as a natural-like barrier against substantially stronger lower bounds for general formulas.

Host:  Prof. Alexander Razborov

Refreshments will be served before the talk in Ry 255.

 

 
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